In this paper, we present a variant of discrete Jensen-type inequality for generalized strongly convex functions on a real linear fractal set Rα ( 0 < α ≤ 1). Further, we also demonstrate a generalized Jensen–Mercer type inequality for generalized strongly convex function by employing local fractional calculus. Using this generalized Jensen-Mercer inequality, we establish a Hermite-Hadamard-Mercer type inequalities for generalized strongly convex functions.